Answer
Please see the work below.
Work Step by Step
We can calculate the $v_{rms}$ for $N_2$ at room temperature as follows
$v_{rms}=\sqrt{\frac{3RT}{M}}$
We plug in the known values to obtain:
$v_{rms}=\sqrt{\frac{3(8.314\times 298)}{0.02802}}=515\frac{m}{s}$
We know that
$v_{rms}(He)=\sqrt{\frac{3RT}{M}}$
We plug in the known values to obtain:
$515=\sqrt{\frac{3(8.314)}{0.004003}}$
This simplifies to :
$T=42.5665K$
